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RSA definition

What value of scale factor should be entered in the definition of a response spectrum load case?

Answer: When the response-spectrum curve is defined, acceleration is typically entered as a fraction of gravitational acceleration (9.81 m/sec² or 32.2 ft/sec²). Scale factor should be specified such that its product with response-spectrum values generates the acceleration units desired.

For example, if acceleration for the response-spectrum function is plotted as a fraction of gravitational acceleration, and if length units are in feet, then U1, U2, and U3 should be scaled by 32.2 units.

How are multiple response-spectrum curves defined?

Answer: Multiple response-spectrum curves may be defined using Named Set and interactive database editing to generate results in tabular format. The steps to do so are as follows:

1. Define one response-spectrum curve, then save the definition by selecting Save Named Set.
2. Use the interactive database editor to create the remaining Named Sets, one for each plot, by editing the tables within Model Definition > Other Definitions > Named Sets.
3. Display the output table by selecting Analysis Results > Structure Output > Named Set Data.

Can damping be changed without modifying the response-spectrum function?

Answer: Yes, the response-spectrum function damping ratio and modal damping ratio may be specified. Modal damping ratio may be increased such that damping increases without the need to change the response-spectrum function. Additional information is available in the Damping in response-spectrum analysis article.

RSA application

How is response-spectrum analysis applied only above grade?

Answer: During response-spectrum analysis, loading is applied to the entire structure, though sub-grade modes will have much higher frequencies, providing minimal contribution to modal response. However, the mass participation of subgrade levels may be subtracted from the total mass.

RSA deflection

Why is deflected configuration identical for acceleration loads applied in either direction?

Extended Question: Acceleration loads are applied along U1 first with a 10° angle, then with a -10° angle. Why does response-spectrum analysis generate identical deflected shapes for either orientation?

Answer: For each response quantity and realization of structural period, response-spectrum analysis generates a single positive result for the likely maximum response of a structure subjected to a loading condition. If the structure is symmetric, results should be identical regardless of loading orientation because absolute values are taken during numerical formulation.

Additional information is available in the CSI Analysis Reference Manual (Response Spectrum Analysis, page 339).

Why does the deflected shape for a linear-add load combination not look correct?

Answer: Response-spectrum analysis generates the likely maximum response that a structure may experience in either direction. The deflected shape for a linear-add load combination which contains a response-spectrum load case will display either the minimum or maximum displacements, depending on which has the greater absolute value. Depending on the sign of loads within the load combination, displacement may be in the positive or negative direction, even for adjacent joints.

See also Deformed shape for moving load analysis.

RSA output

How are response spectra and resultant forces obtained for each mode?

Answer: The response contribution from each mode is available through Display > Show Tables > Analysis Results > Structure Output > Modal Information > Table: Response Spectrum Modal Information.

Response-spectrum modal amplitudes (U1Acc, U2Acc, U3Acc, U1Amp, U2Amp and U3Amp) give the mode-shape multipliers which contribute to structural displacement for each direction of Acceleration. For a given mode and direction of acceleration, amplitude is the product of modal participation factor and response-spectrum acceleration, then divided by the Eigen value (ω2) of the mode. When amplitude is multiplied by any modal response quantity (displacement, velocity, acceleration, force, stress, etc.), this value represents the contribution of a given mode to the same response-quantity value reported for the response-spectrum load case.

Please note that mass is always normalized for modes, based on the database units chosen when a new model is created from templates. The GUI environment is also set to these units, as shown in the Units Box in the bottom-right corner of the display window. While interpreting results, modal amplitudes should be consistent with these database units.

How are response-spectrum curves generated from an acceleration record?

Answer: For response, please see the Derivation of response-spectrum equations article.

Can SAP2000 develop response spectra for a given location within the structure?

Answer: Yes, please see the Generating response-spectrum curves article for response.

Why are Von Mises stresses not computed and plotted during response-spectrum analysis?

Answer: Von Mises stresses are computed only when results have correspondence. Response-spectrum forces do not have correspondence when modal combinations are performed. As a result, design will proceed according to the force envelope, which is a function of the maximum values for P, M2, and M3. In reality, these maximum forces do not occur simultaneously, therefore no plot is available. If necessary, post-processing is available for modal results.